the disclaimers must be on the digital and physical documents. not everyone who will ever handle them will know their origin, authenticity, or how to validate them.
however, there are plenty of things in civil and structural engineering that carry a huge amount of liability, and do in fact need to be done by a licensed/insured professional. for example, where electrical wiring or sewage pipes are buried. getting a property line wrong, in some cases can be a big problem.
A drawing of your property boundary so you can know where to mow the lawn to or find a plot of acreage granny left you isn't an engineering or legal document and shouldn't be treated as one.
A reasonable person could confuse the plans produced by the website and legitimate plans produced by a professional surveyor, though.
More to the point, the author of the website seems to disagree with you, since he already includes a disclaimer on the website. The issue raised is that he does not include that same disclaimer on the plans.
GP's phrasing of 'everyone who will ever handle' the plans is the correct phrasing: those are the people that must be considered. That group includes all people whose work and interests require knowing where property boundaries and physical structures are, now, and in the future.
The professional engineering and survey boards have a duty to the protect the public, and a duty to regulate the practice of land surveying and civil engineering. If someone's behavior interferes with that practice, then they have a legitimate cause to prevent that behavior.
The disclaimer on the website is so buyers know what they're getting and don't waste money on something that isn't adequate for their legal/planning needs.
Your interpretation of the disclaimer may be correct, but the phrasing "This is not a Legal Survey, nor is it intended to be or replace a Legal Survey." is excessive for that purpose and makes more sense if it's meant to head off complaints from the engineer's association.